Not sure how relevant this information is, but I've been having this issue in other games as well, or at the very least in other games after having played the finals in the same session.
FWIW I am also Fedora 41, with a 6950XT

For what its worth, there also seems to be a threading issue in The Finals too...

If you watch the output of btop for example, the number of threads in Discovery.exe will continue to grow until you quit the game.

I have the exact same issues and symptoms in the finals since yesterday. I am using proton experimental and proton 9.0-4. There is no fps drop issue in other games (after launching the finals).

My system information:
Kernel Version: 6.11.11-1-MANJARO
CPU Brand: AMD Ryzen 9 7900X3D 12-Core Processor
Driver: AMD AMD Radeon RX 7900 GRE (radeonsi, navi31, LLVM 18.1.8, DRM 3.59, 6.11.11-1-MANJARO)
Driver Version: 4.6 (Compatibility Profile) Mesa 24.2.8-arch1.1

Please tell me if I should provide more information.

Fairly certain this isn't a vkd3d issue as the same issue occurs when using the DirectX 11 backend (-dx11 launch option) of the game which would use dxvk.

Also observing perf-top shows no symbols related to radv or vkd3d. It actually shows practically no difference between the time when it stutters and runs normally.

For what its worth, there also seems to be a threading issue in The Finals too...

If you watch the output of btop for example, the number of threads in Discovery.exe will continue to grow until you quit the game.

I can see evidence of that in the proton logs as well, it's renaming threads and I see logs similar to this in relation to fps drops:

47466.568:01cc:01d0:warn:seh:dispatch_exception backtrace: --- Exception 0xc0000005.
47466.568:01cc:01d0:trace:seh:dispatch_exception code=c0000005 flags=0 addr=00007000005C3E2C ip=7000005c3e2c
47466.568:01cc:01d0:trace:seh:dispatch_exception  info[0]=0000000000000000
47466.568:01cc:01d0:trace:seh:dispatch_exception  info[1]=00007fd731826000
47466.568:01cc:01d0:warn:seh:dispatch_exception EXCEPTION_ACCESS_VIOLATION exception (code=c0000005) raised
47466.568:01cc:01d0:trace:seh:dispatch_exception  rax=0000000000b9e600 rbx=0000000000c71140 rcx=0000000000b9e600 rdx=00007fd731826000
47466.568:01cc:01d0:trace:seh:dispatch_exception  rsi=0000000000b9e600 rdi=0000000000c86562 rbp=0000000000b9d270 rsp=0000000000b9d1e8
47466.568:01cc:01d0:trace:seh:dispatch_exception   r8=0000000000000040  r9=0000700000009910 r10=0000700000000000 r11=00000000ffffffbf
47466.568:01cc:01d0:trace:seh:dispatch_exception  r12=0000000000bcdd60 r13=0000000000c83921 r14=0000000000b9e648 r15=00007fd731826000
47466.568:01cc:01d0:warn:seh:virtual_unwind backtrace: 0000700000DCEC3F: unknown module.

Fairly certain this isn't a vkd3d issue as the same issue occurs when using the DirectX 11 backend (-dx11 launch option) of the game which would use dxvk.

Also observing perf-top shows no symbols related to radv or vkd3d. It actually shows practically no difference between the time when it stutters and runs normally.

Regarding DX11, I've tried to play with it on Windows and it looks like devs didn't even bother optimizing it, becauze the stutters are like EVERY SECOND. And on Linux (I have 4060 laptop), I get TWICE as less FPS as on Windows. Interestingly, if I start the game for the first time, the FPS seems pretty normal, but change settings and it will drop significantly and never go back (I didn't test it after the menu, though). So yeah, seems like The Dying game FINALS issue there

Unless the devs themselves have pointed at it as a option then i would not regard the dx11 mode as supported.

There isn't any sort of shader precompilation on the dx11 mode in the FINALS. This is pretty much the cause of the stutters. Its is pretty evident that -dx11 was never meant for actual use and is not supported. It is probably just left there as a debugging tool of sorts.

There is no reason for the game to support dx11 as any hardware that doesn't support dx12 can probably not even run the game optimally.

I honestly hate it when people use debugging flags and convars in games and suddenly it starts running worse and they complain. And then the devs just decide to remove or hide these flags to avoid confusion, affecting people who might use these flags for other reasons.

Seems like there was an update to the game which apparently made the game run like crap under proton.

Update from Embark:

We appreciate your observations and for letting us know your concerns.

At this time, THE FINALS is still unsupported in Linux, so our troubleshooting guides may be a little limited. But you can rest assured that our team is always looking into smoothing out the game's overall performance. Input such as yours allows and guides us to understand the opportunities we can strengthen and those that we can improve still. Thank you for sharing your thoughts.
I'll make sure to forward this to our game team for further review regarding the game's development.

If you have further questions or issues encountered in the game, don't hesitate to let us know or send footage for us to determine the necessary action to take.

Feel free to drop by in our official Discord server if you're interested in getting real-time updates about the game's development, patch notes, and news!
https://discord.gg/thefinals

Can confirm. Playing today, I have no FPS issues.